It's not necessarily a matter of fact checking, but of correcting for systemic biases in the data. That's often not the easiest thing to do. Systems run by humans often have outcomes that reflect the biases of the people involved.

The power of suggestion runs fairly deep with people. You can change a hiring manager's opinion of a resume by only changing the name at the top of it. You can change the terms a college kid enrolled in a winemaking program uses to describe a white wine using a bit of red food coloring. Blind auditions for orchestras result in significantly more women being picked than unblinded auditions.

Correcting for biases is difficult, and it's especially difficult on very large data sets like the ones you'd use to train chatgpt. I'm really not very hopeful that chatgpt will ever reflect only justified biases, rather than the biases of the broader culture.